Robust MU-MIMO transmission using virtual UEs

ABSTRACT

Ways to mitigate problems caused by too narrow transmission zero (nulls) without significantly increasing computational complexity. For example, the problem can be mitigated by modifying MU-MIMO transmission schemes so that the nulls are widened. This way, the UEs that are to be protected from transmission interference stay within the nulls, despite the angular disturbances.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a National stage of International Application No.PCT/SE2018/050286, filed Mar. 21, 2018, which is hereby incorporated byreference.

TECHNICAL FIELD

Disclosed are embodiments related to multi-usermultiple-input-multiple-output (MU-MIMO).

BACKGROUND

In the emerging fifth generation (5G) cellular systems, beamforming andmultiple-input-multiple-output (MIMO) transmission will be centraltechnologies. The reason for this is that spectral resources are runningout at low carrier frequencies and this leads to a gradual migrationinto higher frequency bands (e.g., the millimeter-wave (mmw) bands). Atthese high frequency bands beamforming and use of massive antenna arraysare needed to achieve a sufficient coverage. There is, for example,plenty of available spectrum around 28 GHz and 39 GHz in the US andother markets. This spectrum needs to be exploited to meet theincreasing capacity requirements. The 5G frequency migration is expectedto start at 3.5-5 GHz, and then continue to these 28 GHz and 39 GHzbands that are expected to become available relatively soon.

1. Beamforming and MIMO in General:

Beamforming and MIMO transmission is a mature subject today. Thissection just aims at presenting the basics, for a detailed treatment anytextbook on digital communications could be consulted.

To explain the beamforming concept, consider FIG. 1 which shows anidealized one-dimensional beamforming case. In this case it is assumedthat a user equipment (UE) 101 (i.e., a device capable of wirelesscommunication with a radio access node, such as a base station) islocated far away from a radio access node 105 having a plurality ofantennas 102 (i.e., an antenna array). It follows that the difference intravel distance from the radio access node 105 to the UE 101, betweenadjacent antenna elements, is l=kλ sin(θ), where kλ is the antennaelement separation. Here k is the separation factor which may be 0.5-0.7in a typical correlated antenna element arrangement. This means that ifa reference signal s_(i)e^(jωt) transmitted from the i:th antennaelement will arrive at the UE antenna as a weighted sum

$s_{UE} = {{\sum\limits_{i = 0}^{N - 1}{s_{i}h_{i}e^{j\;{\omega{({t - \frac{il}{c}})}}}}} = {{e^{j\;\omega\; t}{\sum\limits_{i = 1}^{N - 1}{s_{i}h_{i}e^{{- j}\frac{{ik}\;{\lambda s}\; i\;{n{(\theta)}}}{f_{c}\lambda}}}}} = {e^{j\;\omega\; t}{\sum\limits_{i = 1}^{N - 1}{s_{i}h_{i}{e^{{- j}\frac{{iks}\; i\;{n{(\theta)}}}{f_{c}}}.}}}}}}$Here ω is the angular carrier frequency, h_(i) is the complex channelfrom the i:th antenna element, t is the time, and f_(c) is the carrierfrequency. In the above equation θ and h_(i) are unknown. In case of afeedback solution, the UE therefore needs to search for all complexchannel coefficients h_(i) and the unknown angle θ. For this reason, thestandard defines a codebook of beams in different directions given bysteering vector coefficients like w_(m,i)=e^(−jf(m,i)), where mindicates a directional codebook entry. The UE then tests each codebookand estimates the channel coefficients. The information rate achievedfor each codebook entry m is computed and the best one defines thedirection and channel coefficients. This is possible since s_(i) isknown. The result is encoded and reported back to the base station. Thisprovides the base station with a best direction (codebook entry) andinformation that allows it to build up a channel matrix H. This matrixrepresents the channel from each of the transmit antenna elements toeach of the receive antenna elements. Typically, each element of H isrepresented by a complex number.

The channel matrix can then be used for beamforming computations, or thedirection represented by the reported codebook entry can be useddirectly. In case of MIMO transmission the MIMO beamforming weightmatrix W needs to be determined so that a best match according to acriterion is met.

2. Reciprocity Based CSI Estimation:

Channel reciprocity is a consequence of Maxwell's equations. Given twonodes (e.g, a UE and a base station) equipped with antenna arrays thatcommunicate in a single frequency band, the channel reciprocity propertymeans that at any given point in time, the complex channel coefficientbetween any transmitting antenna element in one node and any receivingantenna element in the other node, is the same (to within a transpose)in the uplink and the downlink. The channel matrix hence remainsessentially the same between the antenna arrays of the two nodes whenthe direction of the transmission is reversed. It is noted that the timeis assumed to be (almost) the same for the two directions oftransmission.

To exploit reciprocity, the channel coefficients can be directlyestimated by the base station from UE uplink transmission of known pilotsignals, for example so called sounding reference signals, SRSs. Theestimated channel can then be used to compute the combining weightmatrix with a selected principle, and then used for downlinktransmission. This works since the uplink and downlink channels are thesame (to within a transpose) when reciprocity is valid.

3. MU-MIMO by Inversion of the Channel Matrix (H):

A very simple MU-MIMO scheme is so called Zero-Forcing (ZF)transmission. This scheme is sensitive and structurally limited sincethe number of antenna elements in the transmitter and receiver needs tobe equal. It is however very straightforward and easy to compute. Thebeamforming weights W are then obtained from the estimated quadraticchannel matrix H from the condition that the received signal vector sshould equal the transmitted one x, i.e. s=HWx=x, ∀x⇔W=H⁻¹.

This choice thus makes the received data streams orthogonal in theory,provided that H is square and invertible.

4. MU-MIMO with RAT

For so called Reciprocity Assisted Transmission (RAT) the transmissionscheme can be obtained by criterion minimization. In this case it is notneeded that the estimated channel matrix Ĥ is a square matrix. Thestandard RAT criterion to be minimized is then

$\begin{matrix}{\hat{W} = {\underset{W}{argmin}{{{\hat{H}W} - H^{ref}}}_{fro}^{2}}} \\{= {\underset{W}{argmin}{{{\left( {\hat{H} + \overset{\sim}{H}} \right)W} - H^{ref}}}_{fro}^{2}}} \\{{= {\underset{W}{argmin}{{tr}\left( {\left( {{\hat{H}W} - {H^{ref}X{\hat{H}}^{DL}W} - H^{ref}} \right)^{H} + {W^{H}\hat{\Gamma}\; W}} \right)}}},}\end{matrix}$where {circumflex over (Γ)} is the estimate of the covariance matrix of{tilde over (H)}^(DL), and where it is assumed that Ĥ and {tilde over(H)} are uncorrelated. The minimizer of the criterion can beanalytically computed asŴ=((Ĥ)^(H) Ĥ+{circumflex over (Γ)})⁻¹(Ĥ)^(H) H ^(ref).

Here H^(ref) is the desired channel matrix after the beamformingcomputations and the subscript fro denotes the use of the Frobeniusnorm.

SUMMARY

This disclosure is focused on improved ways to address the beamformingopportunities that arise in both the high mmw frequency bands and thelower 4G and 5G bands, below 6 GHz. A problem with operating in thesebands is that very narrow transmission scheme nulls may reduce theperformance of multi-user MIMO (MU-MIMO) transmission schemes. Theproblem is caused by the nulls having a much more narrow extension inthe angular domain, than the impairments like beam weight quantizationand phase noise.

The problem associated with the narrow nulls associated with MU-MIMO canbe illustrated as follows. Consider a scenario with one gNB (i.e., a 5Gbase station) and two UEs with two TX antennas in the gNB and one RXantenna per UE. Beam patterns like the one in FIG. 2 and FIG. 3 thenresults in case of perfect channel knowledge. As can be seen sharp nullsare placed in the directions of the “other” UE to minimize cross-talkinginterference. However, this strategy is known to be non-robust in thepresence of channel estimation errors due to, for example, beam weightquantization or phase noise. The consequence is that MU-MIMO obtained,for example, with RAT may deteriorate to an unacceptable level. Toillustrate this fact, a random angular error of 5 degrees, 1-sigma, wasadded to the scenario. The effect is shown in FIG. 4 and FIG. 5. As canbe seen, the null-forming breaks down completely, with variations andSINR losses exceeding 40 dBs!

Embodiments described here are focused on ways to mitigate theseproblems caused by too narrow transmission zero (nulls) withoutsignificantly increasing computational complexity. For example, theproblem can be mitigated by modifying said MU-MIMO transmission schemesso that the nulls are widened. This way, the UEs that are to beprotected from transmission interference stay within the nulls, despitethe angular disturbances.

In one embodiment, an estimated channel model is augmented withadditional steering vectors representing virtual UEs with their steeringvectors slightly perturbed in angle, as compared to the real UE fromwhich they are constructed. A typical scenario, as shown in FIG. 6, isthat virtual UEs 601 a-601 d (dotted lines) are added in pairs on eachside (in angle) of each real UE (shown in solid). As shown in FIG. 6,virtual UEs 601 a and 601 b are added on each side (in angle) of UE1,and virtual UEs 601 c and 601 d are added on each side (in angle) of UE2. Embodiments further include means for computation of said perturbedsteering vectors of said virtual UEs, and means for addition of apre-selected amount of multiple virtual UEs by means of new schedulingfunctionality.

The idea with the virtual UE addition is also that the virtual UEs needto remain undisturbed by a transmission to another real UE than the onethat generated said virtual UEs. This means that the RAT transmissionscheme needs to create nulls also in the directions of the virtual UEs.Since the virtual UEs, in a preferred embodiment, are selected to beclose (in angle) to the real UEs, the overall effect is expected to be ajoint angular null, covering both the real UE and all virtual UEsgenerated from it. The consequence is widened nulls around the real UEdirections.

Accordingly, in one aspect there is provided a method for wirelesslytransmitting data to a first (UE). The method includes obtaining a firstchannel matrix for the first UE, a second channel matrix for a secondUE, and a third channel matrix for a first virtual UE associated withthe second UE. The method further includes forming a final channelmatrix, Ĥ^(V), comprising the first channel matrix for the first UE, thesecond channel matrix for the second UE, and the third channel matrixfor the first virtual UE. The method also includes using Ĥ^(V) tocompute a set of beamforming weights, Ŵ^(V), and transmitting the datato the first UE using the set of beamforming weights, Ŵ^(V).

In some embodiments, the method also includes obtaining a fourth channelmatrix for a second virtual UE associated with the second UE, whereinthe final channel matrix, Ĥ^(V), further comprises the fourth channelmatrix for the second virtual UE.

In some embodiments, using Ĥ^(V) to compute the set of beamformingweights, Ŵ^(V), comprises calculating:Ŵ^(V)=((Ĥ^(V))^(H)Ĥ^(V)+{circumflex over (Γ)}^(V))⁻¹(Ĥ^(V))^(H)H^(ref),where {circumflex over (Γ)}^(V) is a covariance matrix of a channelerror matrix, {tilde over (H)}^(V) (or {circumflex over (Γ)}^(V) is anidentity matrix), and H^(ref) is a reference channel matrix.

In some embodiments, H^(ref) is configured such that no transmission ismade to the first virtual UE.

In some embodiments, the method further includes: determining that adifference between a first horizontal direction to the first UE and afirst horizontal direction to the second UE is greater than a threshold;scheduling a transmission to the first UE; and scheduling a transmissionto the second UE, wherein the transmission scheduled for the second UEis scheduled on the same time and/or frequency resource as thetransmission scheduled for the first UE.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments.

FIG. 1 illustrates a TRP communicating with a UE using a high-gain beam.

FIG. 2 is a plot illustrating SINR as a function of angle.

FIG. 3 is a plot illustrating SINR as a function of angle.

FIG. 4 is a plot illustrating SINR as a function of angle.

FIG. 5 is a plot illustrating SINR as a function of angle.

FIG. 6 illustrate the use of virtual UEs to widen antenna nulls.

FIG. 7 is a plot illustrating the SIR of a transmission to a first UE.

FIG. 8 is a plot illustrating the SIR of a transmission to a first UE.

FIG. 9 is a plot illustrating the SIR of a transmission to a first UE.

FIG. 10 is a plot illustrating the SIR of a transmission to a second UE.

FIGS. 11-14 illustrate resulting SIRs for a virtual UE separation of0.01.

FIGS. 15-18 illustrate resulting SIRs for a virtual UE separation of0.02.

FIG. 19-24 illustrate resulting SIRs for UEs having low separation.

FIG. 25 is a flow chart illustrating a process according to oneembodiment.

FIG. 26 is a flow chart illustrating a process according to oneembodiment.

FIG. 27 is a block diagram of a network node according to oneembodiment.

FIG. 28 is a diagram showing functional units of network node accordingto one embodiment.

DETAILED DESCRIPTION

Embodiments described below are explained using a single dimensionaluniform array for the sake of brevity. This disclosure, however, is notlimited to such a scenario and is also applicable to, for example,two-dimension arrays, in azimuth and elevation, as well as to antennaarrays that are not uniform in terms of the antenna element arrangement.

As described above, a problem originates from the fact that thenull-forming transmission schemes may operate by placing zeros on theunit circle that represents the directions to the users. Such zerosexactly on the unit circle lead to an antenna gain that is exactly 0 inthe estimated interfering direction. Unfortunately, the zeros of theantenna diagram become extremely deep and narrow in the angulardimension, and therefore the zeros becomes extremely sensitive toangular errors like beam weight quantization errors and phase noise intransmitters and receivers. In addition, channel estimation errors interms of the phase affects the performance. FIG. 2 illustrates this factclearly.

1. MU-MIMO “Robustification” using virtual UEs

1.1 Overview

It is first assumed that a channel matrix estimate Ĥ to a number of UEsfrom a gNB is available, where

$\begin{matrix}{\hat{H} = {\begin{pmatrix}{\hat{h}}_{11} & \ldots & {\hat{h}}_{1n_{Tx}} \\\vdots & \; & \vdots \\{\hat{h}}_{n_{Rx}1} & \ldots & {\hat{h}}_{n_{Rx}n_{Tx}}\end{pmatrix}.}} & (1)\end{matrix}$

The number of rows n_(Rx) correspond to the total number of UE antennaelements and the number of columns n_(Tx) to the number of antennaelements of the gNB antenna array. It may be the case that reciprocitybased processing is applied, in which the matrix Ĥ that is valid in thedownlink has been obtained from an uplink channel estimate Ĥ^(UL), asĤ=(Ĥ^(UL))^(T). This follows since it is trivial to see the receivingantenna element in the uplink becomes the transmitting one in thedownlink and vice versa, so it follows by reciprocity that the downlinkchannel matrix is obtained from the uplink one by a matrix transpose.Note that a conjugate transpose should not be used, only the simpletranspose

The RAT scheme above does place very sharp nulls in the directions ofthe interfered UEs, a fact that needs to be mitigated in view of thephase accuracy impairments affecting the antenna array. To do so theidea here is to introduce virtual UEs. The channel model contributionsto Ĥ from the virtual UEs are generated as slightly phase perturbed(parts of) the channel estimate of the UE whose null(s) is to bewidened. This means that degrees of freedoms of the gNB antenna array isused to robustify the nulling of interfered UEs. This is achieved bylocating virtual UEs, at both sides of and close to a nulled UE, seeFIG. 6.

1.2 Channel Matrix Augmentation

Consider a channel matrix Ĥ and denote the block corresponding to UE iby Ĥ_(i). With the formulation of (1), it thus holds that:

$\begin{matrix}{\hat{H} = {\begin{pmatrix}{\hat{H}}_{1} \\\vdots \\{\hat{H}}_{N}\end{pmatrix}.}} & (2)\end{matrix}$

It is hence assumed that MU-MIMO for N UEs is investigated. Thenconsider one row ĥ_(n,k) of Ĥ_(n), with complex channel gains ĥ_(n,k,l),k=1, . . . , K_(n), l=1, . . . , L_(n) i.e. assuming K_(n) gNB transmitantennas and L_(n) UE antenna elements for UE number n, n=1, . . . , N.The possibly non-used antenna elements are assumed to be padded withzeros to obtain consistent matrix dimensions, should this be needed.

Then add a total of V_(n) virtual UEs for each UE n. Each of these UEsare to use perturbed versions of the rows of the generating row of thereal UE. There will be V_(n) added rows for each row ĥ_(n,k), althoughit may also be possible to leave out parts of the virtual UE additionfor some rows. Each such virtual UE row is then perturbed with a phaseshift corresponding to Δθ_(n,k,v), v=1, . . . V_(n). For the linearantenna array treated above, this means multiplying each antenna gain ofthe row ĥ_(n,k), by e^(−2πjk(l−1)Δθ) ^(n,k,v) , giving the virtual rows

$\begin{matrix}{{{\hat{h}}_{n,k,v} = {\begin{pmatrix}{\hat{h}}_{n,k,1} & {{\hat{h}}_{n,k,2}e^{{- 2}\pi\;{jk}\;\Delta\;\theta_{n,k,v}}} & \ldots & {{\hat{h}}_{n,k,{L_{n} - 1}}e^{{- 2}\pi\;{j{({L_{n} - 2})}}\Delta\;\theta_{n,k,v}}} & {{\hat{h}}_{n,k,L_{n}}e^{{- \; 2}\pi\;{j{({L_{n} - 1})}}\Delta\;\theta_{n,k,v}}}\end{pmatrix}\left( {\begin{matrix}{\hat{h}}_{n,k,1} & {\sigma\;{\hat{h}}_{n,k,2}} & \ldots & {\sigma^{L_{n} - 2}{\hat{h}}_{n,k,{L_{n} - 1}}} & \sigma^{L_{n} - 1}\end{matrix}{\hat{h}}_{n,k,{L_{n} - 1}}} \right)}},} & (3) \\{\sigma = {e^{{- 2}\pi\;{jk}\;\Delta\;\theta_{n,k,v}}.}} & (4)\end{matrix}$The virtual UE channel estimate for the UE n then becomes

$\begin{matrix}{{\hat{H}}_{n}^{V} = {\begin{pmatrix}{\hat{h}}_{n,1,1} \\\vdots \\{\hat{h}}_{n,K_{n},1} \\\vdots \\{\hat{h}}_{n,1,V_{n}} \\\vdots \\{\hat{h}}_{n,K_{n},V_{n}}\end{pmatrix}.}} & (5)\end{matrix}$The final channel matrix estimate with virtual UEs can therefore bewritten

$\begin{matrix}{{\hat{H}}^{V} = {\begin{pmatrix}H_{1} \\H_{1}^{V} \\\; \\H_{N} \\H_{N}^{V}\end{pmatrix}.}} & (6)\end{matrix}$

1.3. Virtual RAT

The final step is to compute the beam-weights using RAT, but based on(6) asŴ ^(V)=((Ĥ ^(V))^(H) Ĥ ^(V)+{circumflex over (Γ)}^(V))⁻¹(Ĥ ^(V))^(H) H^(ref).  (7)

Note that here {circumflex over (Γ)}^(V) can also be constructedfollowing the steps above, or as a simpler solution using {circumflexover (Γ)}^(V) as an identity matrix of the appropriate dimension tonormalize the RAT equations.

It remains to discuss the selection of H^(ref). This matrix should beselected so that the transmissions are orthogonal between users. Thatmeans that there should be ones in the matrix elements of H^(ref) thatcorresponds to transmission of the signal intended for a UE (e.g.column) and the received signal in said UE (row). In a simple case withone signal for each UE and one receive antenna in each UE, the matrixwould be an identity matrix with a dimension equal to the number of UEs.All other values of H^(ref) needs to be equal to 0. It is also necessaryto note that it is critical to select H^(ref) equal to zero for allmatrix elements corresponding to transmission to virtual UEs, since notransmission shall be performed to these virtual UEs.

2. Evaluation

2.1 Antenna Diagrams and SIRS, 2 Rank 1 UEs, Flat Channel, WellSeparated UEs

A case with a Tx single dimensional (horizontal) antenna array and twoUEs each with a single antenna is assumed. For simplicity, flat channelsare used. The initial case treats UEs located at the angles 0.7 rad and−0.1 rad. The parameters were as follows:

n_(Tx)=32, n_(Rx)=2, k=0.5, {circumflex over (Γ)}=10⁻⁸I, ρ=0.999.

Here the parameter ρ can be used as outlined in the invention P 73304(International Publication Number: WO 2019/125240 A1; Publication Date:27 Jun. 2019) which is hereby included by reference. FIG. 7 and FIG. 8display the resulting antenna diagrams, expressed as signal tointerference ratios (SIRS), without any virtual UE addition. The nullscan be seen, however these are as narrow as the sidelobes that are alsoquite deep. To mitigate the sensitivity, virtual UEs separated +/−0.02rad from each UE was added. The result can be seen in FIG. 9 and FIG.10. The change appears to have the intended effect, the nulls arewidened while keeping the needed depth and also the SIR in the desiredtransmission directions.

2.2. The Number of And and the Separation of Virtual UEs

To study the effect of the number of virtual UEs and their separation,it is first noted that the virtual UE separation most likely needs to beless than the sidelobe width, in order to suppress sidelobe gainvariation close to the UE. In addition, to achieve a sufficiently widenull, as compared to the angular errors, more virtual UEs are likely tobe needed the larger the antenna array becomes. To study this in moredetail, a case with n_(Tx)=64, UE separations of +/−0.01 and +/−0.02, aswell as 2 or 4 virtual UEs per real UE were studied. The resulting SIRsfor a virtual UE separation of 0.01 appear in FIG. 11 to FIG. 14.

The SIRs for a virtual UE separation of 0.02 appear in FIG. 15 to FIG.18. From these plots it is clear that the modification achieves what itsets out to do—the nulls are widened. No significant losses of SIRoccur, and the width of the nulls seem to be close to 15 degrees when 4virtual UEs are used with a separation of 0.02.

Although the results appear to be promising, it is stressed that themethod consumes degrees of freedom, i.e. layers. In this case a onelayer transmission to 1 UE costs 5 layers in total.

2.3. SIRs, 2 Rank 1 UEs, Flat Channel, Low UE Separation

To study the behavior when the UEs are close, the 64 element antennaarray above is retained, however the UEs are located at −0.1 radians and0.1 radians, −0.05 radians and 0.05 radians as well as at −0.025 radiansand 0.025 radians. The virtual UE separation was +/−0.01 radians and 4virtual UEs per UE was used. The results appear in FIG. 19 to FIG. 24.For the largest UE separation, the nulls are widened. For UEs at +/−0.05radians, there is no longer any gain while the smallest separation leadsto a breakdown of the scheme. It is not possible to do MU-MIMO when theUEs are closer than the width of the nulls, that are in turn determinedby the angular errors.

3. Scheduling and Clustering of UEs and Scheduling of Virtual UEs

Given the above evaluation, the following observations seems to be inorder:

First, it is not a good idea to schedule UEs that are very close in theangular domain, on the same time or frequency resources. The schedulershould provide separation in time and/or frequency whenever: (a) Anyhorizontal directions θ_(i) and θ_(j) to two UEs, UE_(i) and UE_(j),fulfill|θ_(i)−θ_(j)|<th₁, where th₁ is a first threshold, for a uniformhorizontal antenna array arrangement; and/or (b) Any horizontal andvertical directions {θ_(i),φ_(i)} and {θ_(j),φ_(j)} to two UEs, UE_(i)and UE_(j), fulfill|θ_(i)−θ_(j)|<th₁ and |φ_(i)−φ_(j)|<th₂ where th₁ isa first threshold, and where th₂ is a second threshold, for atwo-dimensional antenna array arrangement.

FIG. 25 is a flow chart illustrating a process 2500, according to anembodiment, for wirelessly transmitting data to a first user equipment(UE1) (see e.g., FIG. 6). Process 2500 may begin in step s2502 in whicha network node (e.g., network node 2700 shown in FIG. 27), which may bea radio access node, obtains a first channel matrix for UE1. In steps2504, the network node obtains a second channel matrix for a second UE(UE2). In step s2506, the network node obtains a third channel matrixfor a first virtual UE associated with the second UE (e.g., virtual UE601 c). In step s2508, the network node forms a final channel matrix,Ĥ^(V), comprising the first channel matrix for the first UE, the secondchannel matrix for the second UE, and the third channel matrix for thefirst virtual UE. In step s2510, the network node uses Ĥ^(V) to computea set of beamforming weights, Ŵ^(V). In step s2512, the network nodetransmits the data to UE1 using the set of beamforming weights, Ŵ^(V).

In some embodiments, the process also includes obtaining a fourthchannel matrix for a second virtual UE (e.g., virtual UE 601 d)associated with the second UE, wherein the final channel matrix, Ĥ^(V),further comprises the fourth channel matrix for the second virtual UE.

In some embodiments, using Ĥ^(V) to compute the set of beamformingweights, Ŵ^(V), comprises calculating:Ŵ^(V)=((Ĥ^(V))^(H)Ĥ^(V)+{circumflex over (Γ)}^(V))⁻¹(Ĥ^(V))^(H)H^(ref),wherein {circumflex over (Γ)}^(V) is one of: a covariance matrix of achannel error matrix, {tilde over (H)}^(V), and an identity matrix, andH^(ref) is a reference channel matrix. In some embodiments, H^(ref) isconfigured such that no transmission is made to the first virtual UE.

In some embodiments, the process also includes: the network nodedetermining that a difference between a first horizontal direction tothe first UE and a first horizontal direction to the second UE isgreater than a threshold; the network node scheduling a transmission tothe first UE; and the network node scheduling a transmission to thesecond UE, wherein the transmission scheduled for the second UE isscheduled on the same time and/or frequency resource as the transmissionscheduled for the first UE.

FIG. 26 is a flow chart illustrating a process 2600, according to anembodiment. Process 2600 may begin in step s2602, where a network nodedetermines angles to UEs being served by the network node (e.g., UE1 andUE2 shown in FIG. 6). In step s2604, the network node determines thatUE1 and UE2 should be added to the same UE cluster. For example, asdescribed above, the network node may determines whether |θ₁−θ₂| isgreater than a threshold (th1) and if it is, then UE1 and UE2 may beadded to the same cluster, where θ₁ is horizontal angle to UE1 and θ₂ isthe horizontal angle to UE2. In another embodiment, as described above,the network node determines not only whether |θ₁−θ₂| is greater than athreshold but also whether |φ₁−φ₂| is greater than a threshold, where φ₁and φ₂ are the vertical angles to UE1 and UE2, respectively, and, if atleast one magnitude value exceed the respective thresholds, then thenetwork node may include UE1 and UE2 in the same UE cluster. In steps2606, the network node schedules UE1 and UE2 on the same time and/orfrequency resources. In step s2608, the network node determines whethervirtual UEs should be scheduled with UE1 and UE2. If one or more virtualUEs are to be co-scheduled with UE1 and UE2, then Ŵ^(V) is calculated asdescribed above (step s2610) and then the network node transmits usingŴ^(V) (step s2612), otherwise the beamformer W is computed usingconventional techniques and the network node transmits using W (stepss2614 and s2616).

FIG. 27 is a block diagram of a network node 2700, according to someembodiments. As shown in FIG. 27, network node 2700 may comprise:processing circuitry (PC) 2702, which may include one or more processors(P) 2755 (e.g., a general purpose microprocessor and/or one or moreother processors, such as an application specific integrated circuit(ASIC), field-programmable gate arrays (FPGAs), and the like); a networkinterface 2748 comprising a transmitter (Tx) 2745 and a receiver (Rx)2747 for enabling network node 2700 to transmit data to and receive datafrom other nodes connected to a network 110 (e.g., an Internet Protocol(IP) network) to which network interface 2748 is connected; circuitry2703 (e.g., radio transceiver circuitry comprising an Rx 2705 and a Tx2706) coupled to an antenna system 2704 for wireless communication withUEs); and local storage unit (a.k.a., “data storage system”) 2708, whichmay include one or more non-volatile storage devices and/or one or morevolatile storage devices (e.g., random access memory (RAM)). Inembodiments where PC 2702 includes a programmable processor, a computerprogram product (CPP) 2741 may be provided. CPP 2741 includes a computerreadable medium (CRM) 2742 storing a computer program (CP) 2743comprising computer readable instructions (CRI) 2744. CRM 2742 may be anon-transitory computer readable medium, such as, but not limited, tomagnetic media (e.g., a hard disk), optical media, memory devices (e.g.,random access memory, flash memory), and the like. In some embodiments,the CRI 2744 of computer program 2743 is configured such that whenexecuted by PC 2702, the CRI causes network node 2700 to perform stepsdescribed herein (e.g., steps described herein with reference to theflow charts). In other embodiments, network node 2700 may be configuredto perform steps described herein without the need for code. That is,for example, PC 2702 may consist merely of one or more ASICs. Hence, thefeatures of the embodiments described herein may be implemented inhardware and/or software.

FIG. 28 is a diagram showing functional units of network node 2700according to one embodiment. In the embodiment shown, network node 2700includes: a channel estimation unit 2802 for obtaining a first channelmatrix for the first UE, a second channel matrix for a second UE, and athird channel matrix for a first virtual UE associated with the secondUE; a digital base band unit 2804 for forming a final channel matrix,Ĥ^(V), comprising the first channel matrix, the second channel matrix,and the third channel matrix; a beamweight computation unit 2806 forusing Ĥ^(V) to compute a set of beamforming weights, Ŵ^(V); and atransmission unit for employing a transmitter to transmit the data tothe first UE using the set of beamforming weights, Ŵ^(V).

While various embodiments are described herein, it should be understoodthat they have been presented by way of example only, and notlimitation. Thus, the breadth and scope of this disclosure should not belimited by any of the above-described exemplary embodiments. Moreover,any combination of the above-described elements in all possiblevariations thereof is encompassed by the disclosure unless otherwiseindicated herein or otherwise clearly contradicted by context.

Additionally, while the processes described above and illustrated in thedrawings are shown as a sequence of steps, this was done solely for thesake of illustration. Accordingly, it is contemplated that some stepsmay be added, some steps may be omitted, the order of the steps may bere-arranged, and some steps may be performed in parallel.

The invention claimed is:
 1. A method for wirelessly transmitting datato a first user equipment (UE), the method comprising: obtaining a firstchannel matrix for the first UE; obtaining a second channel matrix for asecond UE; obtaining a third channel matrix for a first virtual UEassociated with the second UE; forming a final channel matrix Ĥ^(V)comprising the first channel matrix for the first UE, the second channelmatrix for the second UE, and the third channel matrix for the firstvirtual UE; using Ĥ^(V) to compute a set of beamforming weights Ŵ^(V);and transmitting the data to the first UE using the set of beamformingweights Ŵ^(V).
 2. The method of claim 1, further comprising obtaining afourth channel matrix for a second virtual UE associated with the secondUE, wherein the final channel matrix Ĥ^(V) further comprises the fourthchannel matrix for the second virtual UE.
 3. The method of claim 1,wherein using Ĥ^(V) to compute the set of beamforming weights Ŵ^(V)comprises calculating: Ŵ^(V)=((Ĥ^(V))^(H)Ĥ^(V)+{circumflex over(Γ)}^(V))⁻¹(Ĥ^(V))^(H)H^(ref), wherein {circumflex over (Γ)}^(V) is acovariance matrix of a channel error matrix Ĥ^(V) or an identity matrix,and Ĥ^(ref) is a reference channel matrix.
 4. The method of claim 3,wherein Ĥ^(ref) is configured such that no transmission is made to thefirst virtual UE.
 5. The method of claim 1 further comprising:determining that a difference between a first horizontal direction tothe first UE and a first horizontal direction to the second UE isgreater than a threshold; scheduling a transmission to the first UE; andscheduling a transmission to the second UE, wherein the transmissionscheduled for the second UE is scheduled on a same time resource, samefrequency resource, or both the same time and frequency resource as thetransmission scheduled for the first UE.
 6. A network node for use inwirelessly transmitting data to a first user equipment (UE), the networknode comprising: a processor; and a memory containing instructionswhich, when executed by the processor, cause the network node to: obtaina first channel matrix for the first UE; obtain a second channel matrixfor a second UE; obtain a third channel matrix for a first virtual UEassociated with the second UE; form a final channel matrix Ĥ^(V)comprising the first channel matrix for the first UE, the second channelmatrix for the second UE, and the third channel matrix for the firstvirtual UE; use Ĥ^(V) to compute a set of beamforming weights Ŵ^(V); andinitiate the transmission of the data to the first UE using the set ofbeamforming weights Ŵ^(V).
 7. The network node of claim 6, wherein thenetwork node is further to obtain a fourth channel matrix for a secondvirtual UE associated with the second UE, wherein the final channelmatrix Ĥ^(V) further comprises the fourth channel matrix for the secondvirtual UE.
 8. The network node of claim 6, wherein using Ĥ^(V) tocompute the set of beamforming weights Ŵ^(V) comprises calculating:Ŵ^(V)=((Ĥ^(V))^(H)Ĥ^(V)+{circumflex over (Γ)}^(V))⁻¹(Ĥ^(V))^(H)H^(ref),wherein {circumflex over (Γ)}^(V) is a covariance matrix of a channelerror matrix Ĥ^(V) or an identity matrix, and Ĥ^(ref) is a referencechannel matrix.
 9. The network node of claim 8, wherein Ĥ^(ref) isconfigured such that no transmission is made to the first virtual UE.10. The network node of claim 6, wherein the network node is further to:determine that a difference between a first horizontal direction to thefirst UE and a first horizontal direction to the second UE is greaterthan a threshold; schedule a transmission to the first UE; and schedulea transmission to the second UE, wherein the transmission scheduled forthe second UE is scheduled on a same time resource, or same frequencyresource, or both the same time and frequency resource as thetransmission scheduled for the first UE.
 11. A network node for use inwirelessly transmitting data to a first user equipment (UE), the networknode comprising: a channel estimation unit configured to obtain: a firstchannel matrix for the first UE, a second channel matrix for a secondUE, and a third channel matrix for a first virtual UE associated withthe second UE; a digital baseband unit configured to form a finalchannel matrix Ĥ^(V) comprising the first channel matrix for the firstUE, the second channel matrix for the second UE, and the third channelmatrix for the first virtual UE; a beamweight computation unitconfigured to use Ĥ^(V) to compute a set of beamforming weights Ŵ^(V);and a transmission unit configured to initiate the transmission of thedata to the first UE using the set of beamforming weights Ŵ^(V).
 12. Anon-transitory computer-readable storage medium comprising instructionswhich, when executed by a processor of a network node for wirelesslytransmitting data to a first user equipment (UE), are capable of causingthe network node to perform operations comprising: obtaining a firstchannel matrix for the first UE; obtaining a second channel matrix for asecond UE; obtaining a third channel matrix for a first virtual UEassociated with the second UE; forming a final channel matrix Ĥ^(V)comprising the first channel matrix for the first UE, the second channelmatrix for the second UE, and the third channel matrix for the firstvirtual UE; using Ĥ^(V) to compute a set of beamforming weights Ŵ^(V);and transmitting the data to the first UE using the set of beamformingweights Ŵ^(V).
 13. The non-transitory computer-readable storage mediumof claim 12, wherein the instructions further perform operationscomprising obtaining a fourth channel matrix for a second virtual UEassociated with the second UE, wherein the final channel matrix Ĥ^(V)further comprises the fourth channel matrix for the second virtual UE.14. The non-transitory computer-readable storage medium of claim 12,wherein using Ĥ^(V) to compute the set of beamforming weights Ŵ^(V)comprises calculating: Ŵ^(V)=((Ĥ^(V))^(H)Ĥ^(V)+{circumflex over(Γ)}^(V))⁻¹(Ĥ^(V))^(H)H^(ref), wherein {circumflex over (Γ)}^(V) is acovariance matrix of a channel error matrix Ĥ^(V) or an identity matrix,and Ĥ^(ref) is a reference channel matrix.
 15. The non-transitorycomputer-readable storage medium of claim 14, wherein Ĥ^(ref) isconfigured such that no transmission is made to the first virtual UE.16. The non-transitory computer-readable storage medium of claim 12,wherein the instructions further perform operations comprising:determining that a difference between a first horizontal direction tothe first UE and a first horizontal direction to the second UE isgreater than a threshold; scheduling a transmission to the first UE; andscheduling a transmission to the second UE, wherein the transmissionscheduled for the second UE is scheduled on a same time resource, samefrequency resource, or both the same time and frequency resource as thetransmission scheduled for the first UE.